Messier, Charles; Phil. Trans. LV, 294 (1766)

Received January 31, 1765.

XXXIII. A Memoir, containing the History of the Return of the famous Comet
of 1682, with Observations of the same, made at Paris, at the Marine
Observatory, in January, February, March, April, May and the
Beginning of June, 1759. By Mr. Messier, Astronomer, Keeper of
the Journals, Plans, and Maps belonging to the Marine of France,
Fellow of the Royal Society in London, and Member of the Society
of Science in Holland; translated from the French by
Matthew Maty, M.D. Sec. R.S.

Read Jan. 9, 1766.

In the predictions of the heavenly phaenomena, which depend on the motion of
the stars, two things are to be considered, viz. the time and the place.
As to the time, when the velocity and direction of the stars in their motion
both apparent and real are known, the time of their different appulses and
aspects may always be foretold, and the accuracy of the calculation depends
on the exactness with which their velocity and their several inequalities are
ascertained. Now it is well known that all the former uncertainty, as to the
exact time of the return of the comet foretold by Dr. Halley, was owing to the
variations it must have undergone from its several situations and approximations
to the planets in its progress thro' the solar system.

Dr. Halley, who was first aware of the unequal returns of this comet in its
former appearances, which he found to have been alternately of 75 and 76 years,
was likewise the first who assigned their true cause. He ascribed it, as I said
above, to the nearer or more distant approaches of the planets of our system;
and having observed that the comet we are speaking of came very near Jupiter in
the summer of 1681, above a year before its last appearance, and remained
several months in the neighborhood of that planet, he judged that circumstance
alone sufficient to have considerably retarded its motion, and prolonged the
duration of its revolution. Hence he concluded that its return was not to be
expected till the latter end of 1758, or the beginning of the next year.

Dr. Halley observed, in confirmation of this opinion, that the action of Jupiter
upon Saturn is alone sufficient to alter the duration of Saturn's period one
full month; and he adds, how much greater irregularities must not a comet be
liable to, which at its remotest distance gets near four times farther from the
Sun than Saturn, and whose velocity in drawing near the sun needs but a very
small increase to change its elliptic into a parabolic curve.

Dr. Halley does not determine more exactly the time of the return of the comet
of 1682; neither could he do it but by determining exactly the effect of the
neighborhood of Jupiter, which must very sensibly affect the velocity with which
the comet was moving towards the sun. Besides, regard must be had, not only to
this approach to Jupiter in 1681, but likewise to the other approaches to this
and all the other planets, which act upon the comet, as they do upon each other.
In short, it was necessary to consider all the different situations and
distances of all the planets with regard to the comet, during the whole of its
last revolution, and even during its former ones, when returns had been found
unequal.

What immense labour ! and what geometrical knowledge did this task not
require ? Mr. Clairaut, of the Royal Academy of Sciences, undertook it; and
his results but differed one month from the observation. No small degree of
exactness this, considering the immensity of the object. In November 1758, he
published his conclusion, which allowed about 618 days more for the period that
was to end in 1759 than the former, whence he inferred that the comet must be
in its perihelion towards the middle of April. He added, however
(Journal des Scavans, Jan. 1759)
"Any one may think with what caution I venture upon this publication, since so
many small quantities unavoidably neglected by the method of approximation may
very possibly make a month diference, as in the calculation of former periods."
It accordingly proved so, the comet having reached its perihelion on the 13th
of March in the morning. Mr. Clairaut has since published the methods and
calculations, by which he has arrived at this conclusion.

The impatience of astronomers, and their desire to prepare for verifying this
prediction of Dr. Halley, had put them upon enquiring for several years in what
part of the heavens this comet was likely to appear; but, being ignorant of the
exact time of its return, they could not determine the spot where it might be
expected to be seen, but by making various suppositions as to the time of its
perihelium. This Mr. Dirck of Klinkenberg, a famous astronomer, Member of the
Society of Sciences in Holland, and a correspondent to the academy of Paris,
had attempted seven or eight years before, having taken the pains to calculate
the principal points of forteen different tracts, which the said comet was to
take, upon as many different suppositions relating to its passage thro' its
perihelium, almost from month to month, from the 19th of June, 1757 to the 15th
of May 1758. Messrs. Pingré and De la Lande proceeded much in the same
manner in the calculations they published in the Memoirs of Trevoux for April
1759, first and second parts, with this difference, that the latter in their
suppositions had taken narrower limits, and nearer to Mr. Clairaut's
determination, who, as I said before, had fixed the return of this comet to the
middle of April.

Mr. De L'Isle, being curious of seeing the comet on its first return, as soon
as it could be discovered by means of refracting or reflecting telescopes,
before it was visible to the naked eye, thought he must proceed in a different
manner from what other astronomers had done, to find out in what part of the
heavens it must be looked for. He considered that it was not necessary to know
the place throughout its whole course, but only at the moment of its
appearance, because, having once found it out, it would be an easy matter
afterwards to trace it thro' its whole progress by observation and calculation.

A full description of this method is to be found in an ample memoir concerning
this comet, which I have laid before the Royal Academy of Sciences at Paris,
and which no doubt will be printed in their collection, together with a
northern hemisphere, by means of which I have been enabled to look for this
comet in the very place of the sky, where it ought to appear; and it was by
the help of this planisphere that I actually discovered the comet from the
marine Observatory at Paris on the 21st of January in the evening, after
searching for it two years successively whenever the sky would permit.
The weather was extremely clear the 21st of January the whole day and evening.
I seized the opportunity, and as soon as the stars were visible after sun-set,
I examined, thro' a Newtonian telescope of four feet and a half [FL], those
places in the sky, where my planisphere showed that the comet was to be
expected. After much pains, I perceived about seven o'clock a light resembling
that of the comet I had observed the year before in August, September, October,
and the beginning of November *.
I immediately made a configuration of this new light with respect to the
neighboring stars, in order to examine the next night whether it had any motion
among the fixed stars. This light appeared pretty large; and in the middle I
observed a nucleus, or bright spot, which was no proof as yet that it was a
comet, as there are some nebulous stars, with a bright spot in the middle.
By the drawing I took of this new light with respect to two neighboring stars,
one of which was the 18th of Pisces, according to Flamstead's [sic] Catalog,
2d edition, of the 5th magnitude, markes with the Greek letter Lambda, the other
a new star of the 8th magnitude, which I ascertained by observation, by
comparing it with the above-mentioned star Lambda of Pisces, its
right ascension for the present time being 352d.13'.5". and its declination
1d.6'.40" N. and is the 28th in the catalog of the stars which have served
to find out he position of the comet, which is to be seen at the end of this
memoir; at 6h.56' true time, the position of the comet in right ascension was
estiamted at 352d.15'.47". and its declination 1s.32'.6". North.

Jan. 22, at the same hour as the day before, the sky being equally clear, I
again saw the same light with the 4 1/2 foot telescope, and found it had
sensibly changed its place, but its appearances were the same. From this
second observation I no longer doubted of its being a comet; and from this
very night I began to take notice of the situation of the nucleus, by
comparing it with a small new star which is not to be found in the catalogs,
nor in the celestial maps of Flamstead [sic], but is that whose position I
have just now mentioned, and which stands No. 28 in the catalog annexed to
this memoir. It was not without some difficulty that I could take the
position of the comet with regard to this little star, because I was obliged
to throw light upon the threads of a silk micrometer, which was adapted to
the Newtonian telescope, four feet and a half long, and the least degree of
light from the wax candle I made use of, presently made both the comet and
the star disappear. The position of the comet may be seen in the second table
hereunto annexed, and likewise all the other positions of it , which have
been determined to the time of its disappearing.

The 23d, the sky being very clear, I again saw the comet; its appearances
were the same as the two preceding days. I compared the nucleus with a very
small star, only of the 10th magnitude, which I have settled by comparing it
with the 46th star or Pisces of the 6th magnitude, according to Flamstead's
catalog. See the position of this star in the first table, No. 27.
The position of the comet is set down in the second table.

The 24th in the evening, the fog, thin clouds, and vapours about the horizon
suffered me to take but an imperfect view of the comet; all I could do to
get at its situation was to observe the differences of azimuths and heights
of the comet, and the two stars of Pegasus called Algenib and
Markab. These differences did not appear to me to be so exact as to
depend upon the determination of the comet from them, so I shall give no
account of them.

The 25th in the evening, the sky being clear at times, I again saw the comet;
its light was increased, and the nucleus looked brighter than before, but
without any appearance of a tail. I compared it directly with a star which
is the 16th of Pisces, in the order of Flamstead's catalog. It was
likewise compared with No. 26 of my table. The comet was sufficiently visible
this night to be seen thro' a common two feet [FL] telescope, and even thro'
one of a single foot [FL]. At four minutes past seven, the comet was still
to be seen thro' the telescope at the height of 13 deg above the horizon.

The 26th, the cloudy weather prevented my seeing the comet; but the 27th, the
sky being tolarably clear, tho' the air was not altogether free from vapours,
I again saw the comet, but could form no judgement of its appearance.
I compared the nucleus with a new star which is the 25th in my table, which
I knew by comparing it with some stars in Flamstead's catalog. I also
directly compared the nucleus with the 16th star of Pisces. See second table.

The 28th, the sky being pretty clear in the evening, I began to see the comet
at 26 1/2 above the horizon; but the air was so much darkened by some
fire-works which had just been played off at the Prince of Conde's, that I
could neither judge its shape nor its brightness. All I could do was to
compare it three times with the new star mentioned above, No. 25 of my table,
and once with th 16th of Pisces.

The 29th and the 30th it was too cloudy to see the comet, but the 31st it
cleared up a little; the comet appeared between the clouds, though not plain
enough to judge of its increase, but only to compare it with two stars, which
are not in Flamstead's maps, nor mentioned in his catalog, but are not far
from the star k of Pisces of the 5th magnitude, with which I compared
them. They are both set down in the first table, No. 23 and 24.

February 1, the sky being perfectly clear in the evening, the comet appeared,
notwithstanding a strong twilight and the neighborhood of the moon. I compared
the nucleus with the same two new stars, No. 23 and 24. The clearness of the
air this night induced me tomeasure the diameter of the coma of the comet with
the micrometer adapted to the Newtonian telescope, and I found it 2 min. and
1/2. I likewise determined the magnitude of the nucleus, which I found to be
20", having compared it with the thickness of one of the threads of the
micrometer, which I afterwards reduced into parts of the micrometer. The
twilight was then such as to favour this measuring and the other observations.

The 2d the clouds prevented my seeing the comet, but the 3d, about sevon
o'clock, the sky being tolarably clear, the comet appeared, though but faintly,
by reason of its nearness to the horizon and of the light of the moon; however,
I compared it with a star of Pisces that is to be found in Flamstead's
catalog. It is the 8th of that constellation, marked with the Greek letter
Kappa'. The position of this star for the present time is shewn in the first
table.

The 4th I was as much hindered as the night before by the comet's nearness to
the horizon, and by the too great light of the moon, which made it impossible
to judge of its increase. I compared the nucleus with the same star Kappa' of
Pisces.

From the 4th to the 11th it was utterly impossible to make any observations,
or even to see the comet, by reason of the clouds which darkened that part of
the sky at the time it should have appeared. The 11th the sky was clear in the
evening. I saw the comet, which was but 10 deg high, so that I could not judge
of its appearance, from its nearness to the horizon, and the strong light of
the moon, which was then at the full. I was likewise much obstructed by the
height of the chimneys which stand between the horizon and the marine
Observatory to the West. This prevented my comparing the comet with the
neighboring stars for a quarter of an hour that it it continued visible. All I
could do was to draw the configuration of these stars with the comet, both with
the four feet and half [FL] telescope and with a little two feet refracting
telescope, which was so flastened over the reflector in a parallel situation.
From this configuration, I have estimated the position of the comet, as seen
in the second table.

The 12th, the sky, which had been cloudy all day, cleared up a little in the
evening. The comet appeared near the horizon for a few minutes, but was soon
hid behind the chimneys. All I could do was to estimate its position relative
to the neighboring stars.

The 13th, the sky was quite overcast,; but the 14th having cleared up in the
evening, I could see the comet, but close to the horizon, at the height of
6 deg for a few minutes; and it soon disappeared, being intercepted by
terrestrial objects too high above the horizon, and which I could not keep
clear of. All I was able to do in the short interval it was visible, was to
take a hasty estimate of its position with respect to the star A of Pisces.
The brightness of the twilight prevented my seeing the comet earlier.

The 15th and the 17th, the sky was pretty clear in the evening; but I could
not see the comet at all, because of the bright twilight, which continued till
the setting of the comet.

The comet no longer being visible at night, on account of its getting into the
sun's rays, Mr. De L'Isle and i examined the exactest observations I had made,
which helped us to determine the time and the place in the sky, where it was
to re-appear in the morning, when it should get clear of the rays of the sun.
This was to happen towards the end of March; but the cloudy weather, which
prevailed at Paris during that month, prevented our seeing it again. Besides
this inconveniency, the marine Observatory did not stand high enough to see it
at its first rising in the morning. We were obliged to look out for a more
convenient place in the neighborhood, and met with one at the house belonging
to the College of Lewis the Great, where there is a turret which overlooks all
the horizon, and where Father Merville, Professor of Mathematics, makes his
observations. The 31st of March I removed thither my 4 1/2 feet Newtonian
telescope, and likewise a pendulum clock.

I spent the night from the 31st to the 1st April in this turret with Mr.
De L'Isle. At three in the morning, I began to trace a meridian upon the floor
by the means of a sea-compass; and I likewise drew a line, which made an angle
of about 74 deg with the meridian, from the South toward the East, in the
direction of which the comet was to first appear. I directed the Newtonian
telescope according to this line; and at 52 minutes past three I saw the comet,
about two degrees above the horizon. It appeared much larger and brighter than
in the middle of February; and indeed it was but 18 days past its perihelion.
Now it is well known that cometsare much brighter after the perihelion than at
the same distance before it. Besides, the comet after passing the perihelion
was as near again to the earth as on the 14th of February, when I lost sight of
it at night. When I saw this comet again on the 1st of April, I could very
plainly discern its tail, but could not ascertain its length, because of the
morning twilight which was then beginning, and soon increased much; it filled
the field of the telescope, and must have extended far beyond. According to
what I have observed, the tail of the comet must have spread to more than 25
degrees. The nucleus was considerable, but not well terminated, and it
apparently exceeded the size [brightness] of a star of the first magnitude.
It was of a pale whitish colour, not unlike that of Venus. The nebulosity which
surrounded the nucleus, and went on lessening, shewed reddish colours, and
these colours grew more vivid toward the brightest parts of the tail. The
morning twilight, which increased apace, soon put an end to these appearances,
and afterwards made the comet itself disappea; however, I had been able to
perceive it with the naked eye when it was somewhat disengaged from the vapours
of the horizon. In this short interval, I had but just time to observe the
shape of the comet with the telescope, and to compare the nucleus with a star
which I have since found to be the 30th of Aquarius, according to Flamstead's
catalog, where it is set down as of the 6th magnitude. The difference of
declination between the star and the comet was only estimated. The true time of
this observation, which will be found in the second table, has been concluded
only by means of a minute watch, which had to be set to the true time in the
evening by the clock of the marine Observatory. This was likewise the case with
respect to the observations made during the month of April, in the turret of
the College of Lewis the Great, where there was a pendulum clock, as I said
before, set by a watch which was regulated every day of observation.

More minute accounts of this comet will be seen in a memoir which I have
presented to the Royal Academy of Sciences at Paris, together with two
celestial maps shewing [sic] the tract of the comet through the fixed stars
during its appearance, which I have traced exactly from my observations.
There is likewise annexed to this memoir a collection of all the
observations which have been made of this comet, by my own and
Mr. De L'Isle's correspondents. These observations have been taken, at the
Hague by Mr. Dirck de Klinkenberg, at Leyden by Mr. Lulof, at Montpelpellier
by Mr. de Ratte, at Avignon by Father Morand, at Vienna by Rev. Father Hell,
at Leipsick at Rome, at Cadiz by Mr. Godin, at Lisbon by Father Chevalier,
and at Pondicherri in the East Indies by Father Coeurdoux.

Explanation of the two Tables annexed to this Memoir.

The first table contains the right ascensions and declinations of the stars,
both of the new ones and of those in Flamstead's catalog, for the time of
the observations. It appears from this table, that the comet has furnished
me with an opportunity of determining the positions of 29 new stars, which
were not yet known, and which have served for the determination of the
comet.

The second table contains all the places of the comet, as well in right
ascension and declination, as in longitude and latitude, concluded from its
situation observed relaticely to the stars, whether new ones or already
known. These are the titles of each column:
The 1st points out the day of the month;
the 2d, the true time for each observation;
the 3d, the right ascensions of the comet observed;
the 4th, the declinations;
the 5th, the longitudes observed;
the 6th, the latitudes;
the 7th, the differences ofpassage in right ascension of the comet and the
stars, marked with the sign "-" [Minus] when the comet preceded the star
or was to the West of it, and with "+" [Plus] when it followed the star or
was to the East. This difference, according to the sign, being either
added or substracted from the right ascension of the star set down in the
first table, with which the comet was compared, will give its right
ascension.
The 8th column shews [sic] the differences of declination between the
comet and the stars, marked likewise with "+" [Plus] and "-" [Minus], and
which, being accordingly either added to or taken from the declination of
the star with which the comet was compared, will give its declination.
The 9th column contains the magnitude of the stars;
and the 10th, which is the last, has Bayer's letters, and the numbers of
the stars, either new or taken from Bayer's catalog, according to their
order in each constellation.

The following are the elements of the comet, as computed by Messrs.
de la Caille, Maraldi, and De la Lande.

TABLE I.

Containing the right Ascension and Declination of the Stars for the Time of
the Observations of the Comet of 1759, both the new ones and those of
Flamstead's [sic] Catalog, which have been made use of to find out the
Positions of the Comet as set down in the next Table.

TABLE II.

Containing the Places of the famous Comet of 1682, discovered at the Marine
Observatory at Paris, January 21, 1759, in the Evening, in the
Constellation of Pisces: concluded from the Situation observed with respect
to the Stars of the former Table.